Saving Function (2)

As we have already understood various components of savings, now here we will understand the saving function graphically. 

Tabular explanation of Consumption function

Y(Rs)	C (Rs)	S ( Y- C)
0 20 40 60 80 100 120	30 35 40 45 50 55 60	-30 -15 0 15 30 45 60

The above table shows:

Like consumption, saving is an increasing function of the level of income, i.e. the amount of saving increases with an increase in the level of income.

1)Since, there is always some minimum level of consumption (C) irrespective of the level of Y, Saving (S) must be negative so long as C > Y

When Y = 0, S = -30.It is a situation of Negative situation or dissaving.

2) S increases as Y increases.

3) When Y = 40, S = 0. Here C = Y. This is Break – even point, when there is no saving.

Graphical Explaination of the Saving function

saving function

1) SS is the saving function, showing the behavior of S with respect to Y.

2) SS is a straight line moving upward showing that SS is a linear function and there is a positive relation between Y and S.

Upward slope indicates that the higher income level leads to higher amount of saving. At low levels of income, saving is negative, and at higher levels of income saving is positive.

3) S = 0 when Y = 40. S is negative as long as C > Y.

Negative saving or dissaving arises because consumption expenditure is higher than the income corresponding to low levels of income.

4) The slope of S line indicates the Marginal propensity to save. Since the saving line is upward sloping so its slope is positive but less than unity.

This indicates that MPS is greater than zero, but less than unity at all levels of income, i.e. MPS is positive.

5) Proportion of income saved, i.e. APS, increases with increase in income. At higher level of income, consumption falls and saving increases (people start saving more).

Algebraic Expression of saving Function

The general equation for a linear saving function is expressed as:

S = -a + sY

Where,

S  : is the saving

a  : represent a negative constant which represent dissaving or negative saving when Y = 0
s  : denotes marginal propensity to save or the slope of the saving line

Y : Income

Let us take few numerical examples:

Example 1:

Find S when a = 200, s(MPS) = 0.4 and Y = 1000

Solution:

We know that

S = -a + sY

We also know that –a (negative saving) is the negative expression of a(autonomous consumption).

Substituting the values, we get:

S = -200 + 0.4(1000)

    = -200 + 400

    = 200

Example 2:

Find out MPC and MPS from the following data.        

Income (Rs)	Saving  (Rs)
100 200	60 100

Solution:

First we will calculate the consumption done

∆Y = ∆C +∆ S

Income (Rs)	Saving  (Rs)	Consumption (Rs)
100 200	60 100	40 100

∆Y = 200 – 100 = 100

∆C = 100 – 40 = 60

MPC = ∆C / ∆Y

         = 60 /100

           0.6

MPS = 1 – MPC

         = 1 – 0.6

         = 0.4

Example 3:

Find saving function when consumption function is given as: C = 500 + 0.5 Y

Solution:

S = -a + sY

Where –a = saving when Y = 0

We also know that –a (negative saving) is the negative expression of a(autonomous consumption).

s(MPS) =  MPS = 1 – MPC

Therefore, S = -500 + (1 – 0.5)Y

                   = -500 + 0.5 Y

Saving Function = -500 + 0.5 Y

Example 4:

Complete the following Table:

Income	Saving	MPC	APS
0 20 40 60	-12 -6 0 6	- - -	- - -

Solution:

Income	Saving	Consumption C = Y - S	MPC = ∆C / ∆Y	APS = S/Y
0 20 40 60	-12 -6 0 6	12 26 40 54	- 14/20 = 0.7 14/20 = 0.7 14/20 = 0.7	- -6/20 = -0.3 0/40=0 6/60 = 0.1